Predictive combinatorial optimization, where the parameters of combinatorial optimization (CO) are unknown at the decision-making time, is the precise modeling of many real-world applications, including energy cost-aware scheduling and budget allocation on advertising. Tackling such a problem usually involves a prediction model and a CO solver. These two modules are integrated into the predictive CO pipeline following two design principles: "Predict-then-Optimize (PtO)", which learns predictions by supervised training and subsequently solves CO using predicted coefficients, while the other, named "Predict-and-Optimize (PnO)", directly optimizes towards the ultimate decision quality and claims to yield better decisions than traditional PtO approaches. However, there lacks a systematic benchmark of both approaches, including the specific design choices at the module level, as well as an evaluation dataset that covers representative real-world scenarios. To this end, we develop a modular framework to benchmark 11 existing PtO/PnO methods on 8 problems, including a new industrial dataset for combinatorial advertising that will be released. Our study shows that PnO approaches are better than PtO on 7 out of 8 benchmarks, but there is no silver bullet found for the specific design choices of PnO. A comprehensive categorization of current approaches and integration of typical scenarios are provided under a unified benchmark. Therefore, this paper could serve as a comprehensive benchmark for future PnO approach development and also offer fast prototyping for application-focused development. The code is available at https://github.com/Thinklab-SJTU/PredictiveCO-Benchmark.